I. Introduction
Relativistic magnetrons have been of interest since the 1970s [1] as high-power microwave (HPM) sources and many ideas were realized to improve their efficiency [2]. These devices are the most promising HPM sources in terms of their microwave generation efficiency and compactness, but some problems need to be solved first. One of the problems that need solution is HPM pulse shortening caused by the explosively formed cathode plasma evolution [3], common to many HPM sources, and which was addressed by ideas such as the transparent cathode [4], the virtual cathode (VC) [5], and the VC with a magnetic mirror [6]. The transparent cathode used a solid cathode made up of a few conducting ribs, placed in front of each resonator, thus reducing the surface of the conductor involved in the explosive emission while increasing the coupling between the microwave field and the drifting electrons. The VC is based on the idea of the squeezed state of an electron beam [7], that is, the low-energy high-density electron charge trapped between two VCs. The disadvantage of producing a VC is that it requires increasing the radius of the tube containing the magnetron. A magnetic mirror is difficult to realize and requires an additional power supply to energize an additional mirror coil. Recently, a novel type of cathode, the split cathode was introduced and tested experimentally [8]. The split cathode consists of a cathode that is placed upstream and outside the magnetron and is connected by an axial rod to a reflector placed downstream from the magnetron. The annular electron beam emitted by the cathode emitter is trapped in the space between the cathode and the reflector and, at the same time, screens the rod from explosive plasma formation. The split cathode is a simple and practical way to realize a VC without the disadvantages mentioned regarding previous VC ideas. The operation of a split cathode as the electron source in a relativistic magnetron was recently experimentally confirmed and revealed that, indeed, using a split cathode mitigates pulse shortening [9].